Three-phase fluid displacements in a porous medium

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2018-12-01 DOI:10.1142/S0219891618500236

P. Andrade, A. J. Souza, F. Furtado, D. Marchesin

引用次数: 2

Abstract

Oil in a reservoir is usually found together with water and gas. Often a mixture of water and gas is used to displace such oil. In this work, we present the Riemann solution for such three-phase flow problem. This solution encodes the dependence of recovery on the injected proportion, the proportion initially present, and the viscosity of the several fluids. We use the wave curve method to determine the Riemann solution for initial and injection data in the above-mentioned class. We verify the [Formula: see text]-stability of the Riemann solution with variation of data. We do not establish uniqueness of the Riemann solution, but we believe that it is valid.

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多孔介质中的三相流体位移

油藏中的石油通常与水和天然气一起被发现。通常使用水和气体的混合物来驱替这种油。在这项工作中，我们提出了这类三相流动问题的黎曼解。该溶液编码了采收率对注入比例、初始存在的比例和几种流体粘度的依赖性。我们使用波动曲线法来确定上述类别中初始数据和注入数据的黎曼解。我们验证了Riemann解随数据变化的[公式：见正文]稳定性。我们并没有建立黎曼解的唯一性，但我们相信它是有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.